What happens if the temperature goes below -20 C? Do they stop working or do they just don´t register anything lower?

While there is some “buffer” in the specified range, generally speaking it’s a limitation of the sensor itself and the battery.  Long term exposure to extremely high or low temperatures will cause damage to the device.  As such we don’t recommend using it if the temperatures you are monitoring will be regularly at or beyond the specified range of the device.